Spanning surfaces in 3-graphs

We prove a topological extension of Dirac's theorem suggested by Gowers in 2005: for any connected, closed surface $\mathscr{S}$, we show that any two-dimensional simplicial complex on $n$ vertices in which each pair of vertices belongs to at least $n/3 + o(n)$ facets contains a homeomorph of $\mathscr{S}$ spanning all the vertices. This result is asymptotically sharp, and implies in particular that any 3-uniform hypergraph on $n$ vertices with minimum codegree exceeding $n/3+o(n)$ contains a spanning triangulation of the $2$-sphere.Comment: 33 pages, 6 figure

Forcing large tight components in 3-graphs

Any $n$-vertex $3$-graph with minimum codegree at least $\lfloor n/3\rfloor$ must have a spanning tight component, but immediately below this threshold it is possible for no tight component to span more than $\lceil 2n/3\rceil$ vertices. Motivated by this observation, we ask which codegree forces a tight component of at least any given size. The corresponding function seems to have infinitely many discontinuities, but we provide upper and lower bounds, which asymptotically converge as the function nears the origin.Comment: 10 pages. Final version accepted by European J. Combi

Lockable Implants

Total joint replacements for implants include a first member configured to attach to a first bone, a second member configured to reside in an adjacent second bone and a locking mechanism. The locking mechanism is configured to (i) lock the first and second members in alignment for full extension or other defined stabilized configuration and (ii) unlock to allow the first and second members to pivot relative to each other for flexion or bending

Lockable Knee Implants and Related Methods

Total knee replacements for hinged knee implants include a tibial member, a femoral member, a hinge assembly having a laterally extending axle configured to hingedly attach the femoral member to the tibial member, and a lock mechanism in communication with the hinge assembly. The lock mechanism is configured to (i) lock the femoral member in alignment with the tibial member for a full extension or other defined stabile walking configuration to thereby allow an arthrodesis or stiff knee gait and (ii) unlock to allow the femoral and tibial members to pivot relative to each other for flexion or bending when not ambulating

Lockable Knee Implants and Related Methods

Total knee replacements for hinged knee implants include a tibial member, a femoral member, a hinge assembly having a laterally extending axle configured to hingedly attach the femoral member to the tibial member, and a lock mechanism in communication with the hinge assembly. The lock mechanism is configured to (i) lock the femoral member in alignment with the tibial member for a full extension or other defined stabile walking configuration to thereby allow an arthrodesis or stiff knee gait and (ii) unlock to allow the femoral and tibial members to pivot relative to each other for flexion or bending when not ambulating

Expert Testimony in Capital Sentencing: Juror Responses

The U.S. Supreme Court, in Furman v. Georgia (1972), held that the death penalty is constitutional only when applied on an individualized basis. The resultant changes in the laws in death penalty states fostered the involvement of psychiatric and psychologic expert witnesses at the sentencing phase of the trial, to testify on two major issues: (1) the mitigating factor of a defendant’s abnormal mental state and (2) the aggravating factor of a defendant’s potential for future violence. This study was an exploration of the responses of capital jurors to psychiatric/psychologic expert testimony during capital sentencing. The Capital Jury Project is a multi-state research effort designed to improve the understanding of the dynamics of juror decision-making in capital cases. South Carolina data (n = 214) were used to investigate the impact of expert testimony on the mitigating factor of mental illness and the aggravating factor of future dangerousness. Ordered logit regression analyses revealed significant correlations (p \u3c .005) between the presence of a defense psychiatrist or psychologist expert witness during the sentencing phase and jurors’ having the impression that the defendant was mentally disturbed. Similar analyses revealed no significant relationship between the presence of state-introduced psychiatric testimony and jurors’ having the impression that the defendant, if not executed, would be violent in the future. These findings seem to contradict the view that psychiatric testimony on future dangerousness in death penalty cases has a powerful impact on jurors. The jurors in this study were significantly influenced, however, by psychiatric/psychologic testimony in the area of a defendant’s mitigating mental abnormality

Expert Testimony in Capital Sentencing: Juror Responses

The U.S. Supreme Court, in Furman v. Georgia (1972), held that the death penalty is constitutional only when applied on an individualized basis. The resultant changes in the laws in death penalty states fostered the involvement of psychiatric and psychologic expert witnesses at the sentencing phase of the trial, to testify on two major issues: (1) the mitigating factor of a defendant’s abnormal mental state and (2) the aggravating factor of a defendant’s potential for future violence. This study was an exploration of the responses of capital jurors to psychiatric/psychologic expert testimony during capital sentencing. The Capital Jury Project is a multi-state research effort designed to improve the understanding of the dynamics of juror decision-making in capital cases. South Carolina data (n = 214) were used to investigate the impact of expert testimony on the mitigating factor of mental illness and the aggravating factor of future dangerousness. Ordered logit regression analyses revealed significant correlations (p \u3c .005) between the presence of a defense psychiatrist or psychologist expert witness during the sentencing phase and jurors’ having the impression that the defendant was mentally disturbed. Similar analyses revealed no significant relationship between the presence of state-introduced psychiatric testimony and jurors’ having the impression that the defendant, if not executed, would be violent in the future. These findings seem to contradict the view that psychiatric testimony on future dangerousness in death penalty cases has a powerful impact on jurors. The jurors in this study were significantly influenced, however, by psychiatric/psychologic testimony in the area of a defendant’s mitigating mental abnormality

Expert Testimony in Capital Sentencing: Juror Responses

The U.S. Supreme Court, in Furman v. Georgia (1972), held that the death penalty is constitutional only when applied on an individualized basis. The resultant changes in the laws in death penalty states fostered the involvement of psychiatric and psychologic expert witnesses at the sentencing phase of the trial, to testify on two major issues: (1) the mitigating factor of a defendant’s abnormal mental state and (2) the aggravating factor of a defendant’s potential for future violence. This study was an exploration of the responses of capital jurors to psychiatric/psychologic expert testimony during capital sentencing. The Capital Jury Project is a multi-state research effort designed to improve the understanding of the dynamics of juror decision-making in capital cases. South Carolina data (n = 214) were used to investigate the impact of expert testimony on the mitigating factor of mental illness and the aggravating factor of future dangerousness. Ordered logit regression analyses revealed significant correlations (p \u3c .005) between the presence of a defense psychiatrist or psychologist expert witness during the sentencing phase and jurors’ having the impression that the defendant was mentally disturbed. Similar analyses revealed no significant relationship between the presence of state-introduced psychiatric testimony and jurors’ having the impression that the defendant, if not executed, would be violent in the future. These findings seem to contradict the view that psychiatric testimony on future dangerousness in death penalty cases has a powerful impact on jurors. The jurors in this study were significantly influenced, however, by psychiatric/psychologic testimony in the area of a defendant’s mitigating mental abnormality

Expert Testimony in Capital Sentencing: Juror Responses

The U.S. Supreme Court, in Furman v. Georgia (1972), held that the death penalty is constitutional only when applied on an individualized basis. The resultant changes in the laws in death penalty states fostered the involvement of psychiatric and psychologic expert witnesses at the sentencing phase of the trial, to testify on two major issues: (1) the mitigating factor of a defendant’s abnormal mental state and (2) the aggravating factor of a defendant’s potential for future violence. This study was an exploration of the responses of capital jurors to psychiatric/psychologic expert testimony during capital sentencing. The Capital Jury Project is a multi-state research effort designed to improve the understanding of the dynamics of juror decision-making in capital cases. South Carolina data (n = 214) were used to investigate the impact of expert testimony on the mitigating factor of mental illness and the aggravating factor of future dangerousness. Ordered logit regression analyses revealed significant correlations (p \u3c .005) between the presence of a defense psychiatrist or psychologist expert witness during the sentencing phase and jurors’ having the impression that the defendant was mentally disturbed. Similar analyses revealed no significant relationship between the presence of state-introduced psychiatric testimony and jurors’ having the impression that the defendant, if not executed, would be violent in the future. These findings seem to contradict the view that psychiatric testimony on future dangerousness in death penalty cases has a powerful impact on jurors. The jurors in this study were significantly influenced, however, by psychiatric/psychologic testimony in the area of a defendant’s mitigating mental abnormality